Circular definitions in Special Relativity?
A synchronisation procedure of ideal clocks at mutual rest must be transitive, symmetric, reflexive and it must remain valid in time once one has adjusted the clocks to impose it. There is no evident a priori reasons why Einstein's procedure should satisfy these constraints. The fact that it instead happens is the physical content of both postulates you quoted.
Actually there is a third physical constraint: The value of the velocity of light must be constantly $c$ when measured along a closed path. This measurement does not need a synchronisation procedure, since just one clock is exploited.
A natural issue show up at this juncture: whether there are synchronisation procedures different from Einstein's one which however fulfill all requirements.
The answer is positive (without imposing other constraints like isotropy and homogeneity) and they give rise to other formulations of special relativity, which are physically equivalent to Einstein's one. (Geometrically speaking, it turns out that the geometry of the rest spaces is not induced by the metric of the spacetime by means of the standard procedure of induction of a metric on a submanifold.)
There are well-known physical situations regarding clocks with non-inertial motion (at rest with respect to each other), where Einstein's procedure cannot be used and other synchronisation procedures must be adopted. The most relevant is the one regarding a rotating platform. If I remember well, the first correct analysis of the problem was proposed by Born.
Velocity is $dx/dt$ not $\Delta x/\Delta t$ so we aren't measuring the speed between two different places and two different times. The velocity is defined at a point. We don't need any form of Einstein synchronisation to define a velocity.
As for what the postulate is telling us: while the postulate is of historical significance it is not a great way to understand special relativity. The fundamental principle behind special relativity is that the line element defined by:
$$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 $$
where $c$ is a constant, is an invariant i.e. it has the same value for all observers regardless of their motion. The invariance of the line element results in all the weird effects associated with relativity like time dilation and length contraction, and it also tells us that the constant $c$ is the speed of light i.e. the first postulate.